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Bending in the space of quasi-Fuchsian structures

Published online by Cambridge University Press:  18 May 2009

Christos Kourouniotis
Christos Kourouniotis
Affiliation:
Department of Mathematics, University of Crete, Iraklio, Crete, Greece
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In [2] I described the deformation of bending a hyperbolic manifold along an embedded totally geodesic hypersurface. As I remarked there, the deformation is particularly interesting in the case of a surface, because a surface contains many embedded totally geodesic hypersurfaces, namely simple closed curves, along which it is possible to bend. Furthermore, for a surface it is possible to extend the definition of bending to the case of a geodesic lamination, by using the fact that the set of simple closed geodesies is dense in the space of geodesic laminations. This direction has been developed by Epstein and Marden in [1].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 1 , January 1991 , pp. 41 - 49
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

REFERENCES

1.Epstein, D. B. A. and Marden, A., Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces, in: Epstein, D. B. A. (ed.) Analytical and geometric aspects of hyperbolic space, Warwick and Durham 1984, London Mathematical Society Lecture Note Series 111 (Cambridge University Press 1987), 113–253.Google Scholar
2.Kourouniotis, C., Deformations of hyperbolic structures, Math. Proc. Camb. Phil. Soc, 98 (1985), 247–261.CrossRefGoogle Scholar
3.Kourouniotis, C., Bending punctured tori. University of Crete, preprint.Google Scholar
4.Lok, L., Deformations of locally homogeneous spaces and Kleinian groups. Thesis, Columbia University (1984).Google Scholar
5.Thurston, W. P., The geometry and topology of 3-manifolds. Duplicated notes, Princeton, 1978–1979.Google Scholar